What is the value of a state when there is a certain probability that agent will die after each step?
The value of a state depends on the policy that you use, so I'll make the assumption here that you're talking about value using the optimal policy. 

According to the optimal policy, the agent would choose to stay in the square (1,1) every time, but since it has a 0.8 probability of actually staying (and 0.2 probability of dying), we can compute the value of the agent using the Bellman equation as:

$$
V(1,1) = 1 + 0.8 V(1,1) + 0.2 V(\text{death state}) \\
\implies V(1,1) = 1 + 0.8 V(1,1) \\
\implies V(1,1) = \frac{1}{1 - 0.8} \\
\implies V(1,1) = 5
$$

There are other ways of deriving the same number (value function has multiple definitions) but they are equivalent.